Claudio Bartocci Knihy

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.

Negli ultimi cento anni matematica e letteratura hanno incrociato il loro cammino innumerevoli volte, troppe perché si tratti soltanto di incontri casuali. Se è vero che entrambe sono attività di "finzione" e consistono principalmente nell'invenzione di mondi possibili, non stupirà questo continuo e fecondo rispecchiamento. Sensibili in modo particolare al fascino della matematica si sono dimostrati poeti, narratori, romanzieri che nulla accomuna l'uno all'altro, se non il fatto che nelle loro opere, con frequenza e in misura maggiore o minore, emergono idee o strutture matematiche, affiorano riferimenti ai numeri transfiniti o alle geometrie non euclidee, balenano metafore costruite su concetti tratti dall'algebra o dalla logica. Tale fascinazione ha prodotto straordinari racconti; questa antologia ne propone ventisei, da Il libro di sabbia di Borges a La biblioteca universale di Kurd Laßwitz, da Tennis, trigonometria e tornado di David Foster Wallace a un Breve ritratto di Alan Turing di Carrière.

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics’ central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between ‘soul and precision.’